Vignesh, do you still need my explanation for the questions? Things regarding principal values, "without using calculator", or even that is meant by cosine inverse of (- sin 2pi/3)?

So sorry I have been busy the entire day yesterday due to classes and I have more classes later on today.

Yes. I need more explanation. Thanks

Why we do pi-pi/6=5pi/6

Thank u so much to helping me in spite of your busy schedule

Remind me to look at this tonight when I am more free after 12 am

I understood already. Cos is in 2nd quadrant. That’s why pi- p/6. Thanks Mr.Eric

In this particular instance, sin 2pi/3 emerges a positive value, so - sin 2pi/3 emerges a negative value.

Supposing cos-1 (- sin 2pi/3) = x, then we have cos x = - sin 2pi/3. This would mean that we are solving for a possible value of x which matches this condition.

With the principal value of cos-1 x lying between 0 radians and pi radians (i.e. 0 degrees 180 degrees), we soon realise that x must be in the first or second quadrant, and the negative value of - sin 2pi/3 tells us that the angle x (i.e. our answer) must lie in the second quadrant.

Well explained. Thanks a lot Mr. Eric